Wave propagation



Sept. i946.

L. TONKS ETAL.

WAVE PROPAGATI ON Filed April 16, 1942 Fig.

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Inventors www se, r wm, L@ oA/t T A |w .w QW@ LAL/T Patented Sept. 17,1946 WAVE PROPAGATION Lewi Tonks and Le Roy Anker, Schenectady, N. Y.,assgnors to General Electric Company, a corporation of New YorkApplication April 16, 1942, Serial No. 439,243

7 Claims. 1

This invention relates to the propagation and control of electromagneticwaves in the range of wave-lengths below one meter, such waves beingdesignated for convenience as centimeter waves.

It is well known that the passage of electromagnetic waves from a firstpropagating region into a second propagating region of differentelectrical characteristics is ordinarily attended by the reiiection of aportion of the incident energy. Such reiiection occurs, for example,when a wave is caused to pass from a section of transmission line havingone characteristic impedance to a section of line having a diiferentcharacteristic impedance, It occurs in another case when a wave passesfrom one dielectric medium into a second medium of diierent dielectricproperties.

It is desirable in many cases to control the amount of wave reflectionoccurring at apparatus transition points, and certain devices, sometimesreferred to as impedance transformers, have been devised for thispurpose. However, impedance transforming devices heretofore availablehave been usable only in special situations and with somewhatinconvenient limitations. It is an object of the present invention toprovide reflection controlling agencies which are applicable in a verywide variety of cases and which are highly iiexible in the matters ofdesign and mode of use.

It is a more particular object of the invention to provide means usablein connection with the propagation of centimeter waves, as abovedefined, for preventing or eliminating and controlling reflection ofsuch waves. As will be more fully explained in the following, specialdiiculties are encountered in this range of wave lengths because of theneed for taking into accurate account certain factors which may beignored at longer Wave lengths.

In general, the invention involves the use of a plurality of transitionelements which by virtue of their dimensions, spacings and otherproperties are able to efect the reilectionless transmission ofelectromagnetic waves from one propagating region to another. In oneembodiment the transition elements employed take the form of two or moredielectric slabs or plates of appropriate configuration and arrangement.In another they comprise discrete impedance-Varying sections spatiallyand dimensionally correlated to assure attainment of the desiredresults, The considerations which determine the proper form andrelationship of the means employed will be described in the followingfor each distinctive case By the use of a reflection-controlling systemwhich embodies several (i. e. two or more) separate transition elementsit is found that many of the limitations inherent in previously usedimpedance transforming methods are avoided. That is to say, therelatively greater numberiof independently variable factors leads togreater freedom in the design of the individual components and togreater flexibility in the matter of adjusting them. Theseconsiderations will become more fully apparent as the details of theinvention are described;

The features of the invention especially desired to be protected hereinare pointed out in the appended claims. The invention itself, togetherwith its further objects and advantages, may best be understood byreference to the following description taken in connection with thedrawings, in which Figs. 1 to 3 are schematic illustrations useful inexplaining the invention; Fig. 4 is a graphical representation ofcertain data of significance in interpreting the invention; Fig. 5illustrates a first exemplary application of the invention; Fig. 5a is asection on line a-a of Fig. 5; and Figs. 6 to 12 show variousalternative applications.

Single surface refiection In explaining the invention it will beconvenient first to refer to a relatively simple case and then to extendthe theory to include more general and complex cases. With this in mind,the line :ru of Fig. 1 may be considered as defining the boundarybetween a first dielectric region or medium of propagation constant h1and a second dielectric region or medium of propagation constant h2. Itis desired to consider the action of an electromagnetic wave whichimpinges on :ro from the left, the direction of propagation of the wavebeing indicated by the arrow A.

It is useful to note preliminarily that under appropriate conditionselectromagnetic Waves may exist in numerous forms. For example, inconsidering free space propagation, plane transverse waves areordinarily assumed. On the other hand, in a wave guide, such as a rod ofdielectric or the space enclosed by a hollow Conductor, confinedultra-high frequency waves may be developed and propagated which haveeld components not only at right angles to the direction of propagationbut also in the direction of propagation, One such wave, which may beproduced, for example, in a hollow 'cylindrical conductor, is theso-called Ho wave which has magnetic components parallel to andtransverse to the direction of propagation and an azimuthally directedelectric component in a plane transverse to the direction ofpropagation. Another type, frequently called the En wave, has lines ofelectric force parallel and transverse to the direction of propagationand has lines of magnetic force azimuthal with respect to the axis ofpropagation. In general, however, any electromagnetic wave may beconsidered as fully specified for most purposes when its classificationis given, and when the magnitude of one of its field components isstated, the remaining components being then readily determinable fromrelatively simple relationships.

' With these considerations in mind, let the Wave indicated by adirected arrow A in Fig. 1 be characterized by the transverse component,

of the electric field associated with it. Here t represents time, isdistance from an arbitrary origin to the left of ro, and h1 is thepropagation constant of the medium 1. If the medium is nondissipative,h1 is ya pure imaginary; otherwise it is complex.

In order to satisfy the boundary conditions at the surface :L'o in Fig.1 we must have in addition to the incident wave a reflected wave h2 isthe propagation constant of the medium to the right of :120. Thecoeicients r and b` are determined by matching the electric and magneticfields at :1:0 according to a wellunderstood procedure. These coeicientsare real in the case of Fig. 1 if the dielectrics are non-dissipative,but in general they are complex. They give both the amplitude and thephase of `the reflected and transmitted waves at :no referred to theincident wave at the same boundary.

For the case of Fig. 1, r and h are found to be The quantity Z in ytheforegoing equations is defined as the ratio of the transverse .electriccomponent of the propagated wave to the transverse magnetic componentfor the particular propagating region under consideration andcorresponds to the characteristic impedance of the propagating system asthat term is customarily employed. (See Electromagnetic Theory by J. A.Stratton, iirsll ed. pp. 282-284). As thus defined, Z is dependent bothupon the intrinsic dielectric properties of the propagating medium andthe boundary conditions of the propagating system. For example, in thecase of a Coaxial conductor transmission line (where the useful wavesare of plane transverse character) where c is the velocity of light, iiis the permeability of the medium between the conductors, lc is thedielectric constant of the medium, and ro and r1 are, respectively, theradii of the outer and inner conductors. On the other hand, in a `wave'guide comprising a single hollow conductor th'e relationship betweenimpedance and guide di- 4 mensions is more complex, being defined asfollows in the case of I-I waves traversing a rectangular wave guidehaving a dimension which is perpendicular to the transverse electricfield and a dimension y which is parallel to the transverse electriceld.

where c, fi, and 7c have the meanings assigned above; a is one-half theoperating wave length, and an is the smallest value which x may assumeand still permit Vpropagation of waves of this wave length'. (For acircular guide 11:11?, and the ratio .1i/:c becomes unity).

T ke-1 G10 y l# For E waves ZE: C/.L

For E waves in guides Z-h.

We notice from vcomparison of Equations 1 and 2 that b=1+r. Although theamplitude of the transmitted wave is greater than that of the incidentwave if Z2 is greater than Z1, the energy transferred by it isnecessarily less. The greater amplitude is consistent with theconsideration that in different media the power density is proportionalnot only to the square of electric amplitude but also the reciprocal ofthe impedance.

The reection and transmission coeflicients are not the same for wavesincident from the right as they .are for those incident from the left.If primed symbols refer to the `former case, we find that Reflection andtrnsmission at a slab We may examine the case of two boundaries byconsidering the arrangement of Fig. 2, in which the space to the left ofm0 is occupied by medium 1, the space between 3:0 and x1 is occupied bya refractive dielectric a, and the space to the right of x1 is occupiedby a medium 2 (which may be the same as or different from medium 1).

Considering the wave situation at the left of xo, we may attack theproblem by summing the multiple reflections that occur at the varioussurfaces as indicated in Fig. 2. In the following, the characters 1' andT represent reection coemcients in the forward and reverse directionsrespectively, b and b represent corresponding transmission coefficients,and the various subscripts identify the surfaces to which thesecoel'lcients are referred.

The complete reected wave,

Arxewt+h1(a:zg) is determined by the reflection coeicient fro UsingEquations 3 and 4 in connection with Equation 6, we i'lnd that T10-trafP Ws For the transmitted wave Atzlewl-hah-:D

a similar calculation gives the transmission coefficient Atz bz bT e-f@1 *l (8) Amo l r :013,16

and using Equations 3 and 4, we have bxubzle-'7 An important case isthat in which media 1 and 2 are identical. Then r (Equation 1) =Re0=nland 1.... -21'9 RFH-za (7") Also, bx0=1+r and bzlr-l-r, so that (1-r2)6*"1'" T1=m Equations 6 to 9a give the amplitudes and phases of thewaves reilected and transmitted by the plate or slab of dielectriccontained between the surfaces :v1 and :170. These amplitudes and phasesare specified at the surface :12o for the reflected wave and at thesurface :ci for the transmitted wave and are referred to the incidentwave at the rst surface. The coefficients of Equations to 9a are ingeneral complex for both dissipative and non-dissipative dielectrics.They completely describe the effect of the dielectric medium between xoand x1 on the incident wave, and there is no need for referring to anyprocess inside this medium once we have them.

For a practical application of the results obtained in the foregoing, wemay rst consider the situation in which the numerator of the right handmemfber of Equation 7 is set equal to zero as follows:

If all the dielectrcs involved are non-dissipative, so that 0 becomesreal, this condition can be satisfled if |r0!=lre1|. (lrol and [fallrepresent the respective absolute values of reo and nl.)

When re0=mp Equation 10 is satisfied provided I0|=-n1r, and whenre0=re1, then suffices. (Here n is an integer or zero.) 1

As we have seen in connection with the derivation of Equation 7a,re0=1^r1 represents the case of a plate of non-dissipative dielectricseparating identical media. Reference to Equation 7 and to theconsiderations stated in the preceding paragraph shows that such a plategives zero reflection (i. e. R1-(1'e0-l-1'e1e2f)=0) when the plate isany integral number of half wave lengths thick (i. e. when |6|=n1r) Froma practical standpoint it is important to note further that wherenondissipative media are concerned, the condition of zero reflectionautomatically implies a condition of complete transmission (i. e. inaccordance with energy conservation requirements). This is aconsideration the value of which will become more apparent in thefollowing.

Consideration of Equation 1 will show that for rx0=rz1, v(the second ofthe two cases proposed in the next to last paragraph) the media onopposite sides of the refractive plate must be of different impedanceand the plate must have an impedance which is the geometrical mean ofthe impedances of the media which it separates. Assuming this conditionand assuming the further condition that the plate is an odd multiple ofa quarter of the operating wavelength (in the refractive plate) inthickness (i. e.

where n is an odd integer, including unity) we see from (10) that theplate in question may be used to introduce a wave without reflection (i.e. with complete transmission) from the first of the separated mediainto the second. This result holds stricth7 only for non-dissipativedielectrics but is easily corrected to take into account appreciabledissipation in one or more of the media, and the resulting correction issmall. A matching plate may thus be used to introduce a wave withoutreflection into a dissipative medium where it may be totally absorbed.

The maximum reflection obtainable from a non-dissipative plateseparating identical media occurs when #meng Then, by Equation 1 inEquation 7a.

between the value indicated by :1111 and the value indicated by Two 0rmore4 slabs For the case to which the present invention especiallypertains, namely, in which two or more refractive elements are involved,a system such as that illustrated in Fig. 3 may be considered. In thisfigure the refractive regions a and b are understood to -be includedbetween two pairs of separate reference surfaces xo, :1:1 and x2, xs. Weshall assume that the refractive regions a and b are completelyspecified by known coefcients ra, ra, ba, ba, applying to a as a -wholeand rb, T'b, etc. applying to b. These coefficients are analogous to thereection and transmission c0- eilcients for the surfaces of a singleslab as previously derived (e. g. in Equations 7a and 9a).

Following an analytical procedure similar to that used above, we nd thatthe overall reflection and transmission coefficients for the systemwhich includes the two refractive regions a and b are formally of thecharacter indicated by VEquations 6 and 9, being specified as follows:

These formulas apply to dissipative as well as to non-dissipativedielectrics and in general are complex for both cases.

Since we have the reection and transmission coefficients for singleslabs (Equations 7 and 9), we may use them in Equations 12 and 14 toinvestigate the useful properties of pairs of slabs. In this connectionconsider two identical nondissipative plates immersed in anon-dissipative medium of different impedance in an arrangementgenerally similar to that of Fig, 3. Under these circumstances the R1and T1 of Equations 7a, and 9a are respectively the n, ra', Tb and the(Equations 15 and 15a are obtainable by expanding the right-hand membersof Equations '7a and 9a into their real and imaginary components andthen evaluating the angular arguments of the resulting expressions.)Substitution from 15 into Equations 12 and 14 yields where R2 is theover-all reflection of the two-slab system and Since (2-x1) representsthe slab spacing and since Blf depends directly upon slab thickness, it

will be seen that both these quantities are dominant factors indetermining the total reflection from a multislab system. In otherwords, in any propagating system in which the operating wave length isnot extremely large in comparison with the dimensions of the structuralelements involved, reflection cannot be eliminated, as has beenpreviously suggested by various writers, solely by a quarter wavespacing of refractive elements.

Except for the factor eif, Equation 19 is formally the same as that fora single plate (see Equation 7a). By setting the numerator of itsright-hand member equal to Zero (i. e., the condition for zeroreflection) we find that zero reiiection is obtained when where n is aninteger and where, necessarily, l h2 ](x2-i) is greater than zero.

Fig. 4 is a plot of the phase angle, ip, which determines the spacingh2(2-:1:1) in degrees of phase, as a function of the phase thickness, 9,of the plates. The impedance ratio is taken as a parameter.

While it is not immediately evident from Equation 19, it can be shownfrom that equation that R2 is maximum when e*2m=-1. This is an equalitywhich is satisfied when In the event of the fulfillment of thiscondition This is equal to the reflection from a single surface havingan impedance ratio equal to the fourth power of that for the slabs, ascan be seen by substituting from Equation 11 and cornparing it withEquation 1. At the same time it appears that it is equivalent to thereflection from a single slab having an impedance ratio equal to thesquare of that for the two slabs.

Amounts of reflection intermediate between the minimum value of zero andthe maximum value denoted by Equation 21 can obviously be obtained bychoosing spacings between the points dened by Equation 20 and Equation20a. This is an important feature of multislab combinations when usedfor neutralizing reflection from a reflecting boundary outside thecombination since it means that the reflection obtainable with suchcombinations is to a large extent independ ent of the characteristics ofthe individual slabs.

If the two refractive regions are not identical slabs, there is, ingeneral, no separation giving zero reflection. However, in the specialcase inv which l Ta rb l, we nd that no reflection occurs when Ihzl ($21121) (22) In justifying Equation 22 we may rst observe that a conditionto be fulfilled if there is to beI cancellation of the portion of theincident wave which tends to be reected from the first reflecting slab(Fig. 3) is that the various wave components which pass through thefirst slabI and,

. 9: after single or multiple reflection from the second slab, effectrepenetration into medium I mustbe in opposite phase with respect to theprimarily reflected wave. To show that Equation 22 represents thecondition-for a proper phase relationship of the internally reflectedwave components, consider an incident wave of phase zero at :to (Fig. 3)The phase of the primary reection from the rst slab referred to theplane :0 is tba by Equation 15. The phase of the primary transmittedwave at :L'i is by Equation 15a. At :v2 the phase has been advanced byh2 {(:cz-xl) The portion of the wave which is reflected from the slab bis retarded by :pb and this wave is again advanced in phase during itspassage from r2 to x1 by an amount equal to [hz Mrz-x1). Combining allthese phase differences we get for the relative phase of the internallyreected wave at mi. A part of this wave is retransmitted through thedielectric region a into medium I, and a still further portion is againreflected at .r1 and suffers further internal reflections between theboundaries mi and m2. Considering only the portion of the wave which istransmitted through the dielectric a into medium I at the rstopportunity for such transmission, it is apparent that this portion willsuffer a retardation of phase during such transmission of (i. e.,according to Equation 15a). The total phase lag of this part of the wavewhich is available for interference with the primary reflected wave istherefore the algebraic sum of the individual phase diierences:

For this interfering wave to be wholly out of phase with the directlyreflected wave which, as we have seen, has the relative phase angle gba,it is clear that the phase di'erence between the interfering wave partsmust be some odd number of 1r radians. Mathematically expressed, thismeans that This reduces directly to Equation 22. This equation shows,among other things, that reflection cancellation depends upon themaintenance of a proper spacing between the reecting agencies by whichthe cancellation is to be produced. This relationship is true moreover,for all points in medium I since the phase of the two reflected Wavesvaries equally and in the same sense.

Equation 22 can be applied to the problem of introducing a wave from airinto water (neglecting for the moment the slight effect of attenuationon the water reflected wave) by using a refractive slab for a and a.refractive slab backed by water for b. This arrangement is illustratedin Fig. which shows a wave guide in the form of a hollow conductor IDalong which electromagnetic waves are assumed to be propagated. Therelative position of the refractive slabs is indicated at II and I2 andwater backing the slab I2 is shown at I3. It is reasonable to assumethat a material of fairly low impedance may prove suitable for the slabsII and I2 and since quartz is such a material, it will be worth while toinvestigate the possibility of using this substance. If this is at allpossible, it can be done when [rb] (i. e., the reection coeflicient ofslab l2) is a minimum. That this Yoccurs when can be seen from Equation'7, the equation for reection from a single slab, in which now both noand nl are negative because the impedances of the various successivemedia are progressively less in the direction of propagation. Thefollowing data will be used:

A Hm wave having a free space wave length of 10 cm. propagated in a 7.62cm. (3") rectangular guide having a limiting wave length of 15.24

cm. Y

Dielectric constant of quartz 3.6

Dielectric constant of water From these data and by means of knownrelationships (see definitive Equation 2b) We are able to computevarious impedances that we need:

Where subscript 1 refers to the air-lled portion of the wave guide,subscripts a' and b to the slabs II and I2 respectively, and subscript 3to the water-filled section I3; where y and a: are respectively theminor and major dimensions of the wave guide, and where the factor Zo isthe impedance encountered by a plane wave in lfree space. The ratio'yl/m cancels out in the computation of reflection and transmissioncoeiicients and therefore does not require to be numerically specified.)

The reflection coefficients for the various slab surfaces are found byusing Equation 1:

From (7) Now the maximum reflection obtainable from a quartz plate inairis, from (11) Since' this is greater in absolute value than rb,thematching is possible. To make Ira l=| rbl it is only necessary to usea thinner front plate than is indicated by (24). From (7a),

wel:

i 1 In using Equation 22 it should first be recalled that (x3-m2) wasarbitrarily so chosen that is a matter of convenience only. Some othervalue might equally well have been taken in which case the furthertreatment' of the problem would have been complicated to the extent ofhaving to deal with a finite value of rbb throughout.)

Using the impedance ratio Z1/Za=2.'24, Fig. 4 gives yba=118. (Fig. 4shows the variation of 1]/ with 0 for different values of the impedanceratio Zl/Za. For cases where is below. 90 use is made of the upperabscissa scale and the righthand ordinate scale. For cases where 9 isbetween 90 and 180 the lower left-hand scales are used.)

It follows that [h1 l (m2-:131) =121, from which the plate spacing(m2-ain) is, of course, directly determinable.

If the maximum reflection from the plate had not been greater inabsolute value 'than the minimum reflection from plate I2, it would nothave been possible to eliminate reflections with two plates of quartzonly, although the desired result could have been obtained by using amaterial having an impedance closer to that of water. However, by addinga third plate, identical to and positioned ahead of and by applying thegeneral formulas to the resultant three-plate system, it is easy to showthat the range of impedance over which zero reilection may be obtainedis greatly'exten'ded, for, the first two plates then behave like a`single plate with a higher impedance ratio. This arrangement isillustrated in Fig. 6 which indicates a wave guide 2D (either ofcylindrical or rectangular form) containing a series of three mutuallyspaced dielectric slabs 2|, 22, and 23, the plate 23 being backed bywater, as indicated at 24. A special advantage of the three-platearrangement is that not only the impedance but also. the thickness ofthe individual plates may be chosen within much wider limits than ispossible where only two plates are employed. Y

This three-plate matching `apparatus has an analogue in which singlesurfaces replace plates. A wave may zbe introduced without reflectioninto a body of dielectric if` at the proper distance in front of thedielectric we place a refractive plate of the correct thickness. This isindicated in Fig. 7 in which is shown a hollow wave guide 304terminating in a dielectric section 3| and having within its interior adielectric plate 32. Since the condition to be satisfied for zeroreflection is merely that they over-all reflection coefficient of theplate shall equal in magnitude that-of the single surface of dielectric3|, the only restriction on the impedance ratio of the platev (withrespect to the medium in which it is immersed) is that it be greaterthan the squareroot of that. for the dielectric surface (see Equation14) Within these limits a plate of any impedancev may be used providedits thickness and location are properly chosen.

Determination of the proper dimensions and.

location of the plate 32 requires a preliminary determi-nation bymeasurement or computation, of the reflection cceflicient of the surfaceof dielectric 3 W ith this quantity known, the thickness of the platerequired to give an equal coefficient can then be computed. Finally, thespacing of the plate with respect to the dielectric 3| which isnecessary to assure-mutually annihilative interference of the tworeflected wave components may be determined by a procedure like thatused in justifying Equation 22. 'Ihe spacing chosen should, of course,be such that at a plane located in advance of both the plate 32 and thedielectric 3| with reference to the direction of wave propagation, aphase displacement of mr radians exists between reflections attributableto the plate and those attributable to the dielectric, 71. being an oddinteger.

A- single plate such as the plate 32 may alternatively be used to annulreflections due to reflective discontinuities other than a discontinuityattributable toV a change in the propagating dielectric. Examples ofother discontinuities are those produced (l) by a change in dimensionsof a wave guide, or (2) by a change in direction of a waveguide, or (3)fby the junction of a wave guideY with a devicehaving an effectivecharacteristic impedance different from that of the wave guide.

Fig. 8 represents a construction inwhich a wave guide, indicated at 35,is to be employed to conduct waves from. a high frequency source withinwhich such waves are generated. The source, which is indicated in partonly, comprises a metallic enclosure 35 within which are containedelectrode structures 31 such as the electrodes of a split anodemagnetron. The entrance of the wave guide 35 isassumed to be arranged insuch relation to ,the electrodes 31 as to assure that high frequencywave energy will be propagated along the guide.

In order to preserve the vacuum tightness of the container 36 in spiteof the insertion of the wave guide 35, a glass plug 39 is sealed intothe entrance to the wave guide for the purpose of forming a vacuum-tightclosure. In accordance withI the considerations previously given herein,it willfbe understood that the plug 3) constitutes at least a partialbarrier to the passage of waves and may lead to objectionable reflectionof such waves. The geometry of the system in question makes itinexpedient to eliminate such reflection by means of slabs located inthe guide within the container 36. However, an equivalent effect can beobtained by means of a pair of dielectric slabs 4| and 42 arrangedWithin the guide at a point outside the container 35.

In order to determine the proper arrangement of the slabs.4| and 42, itis necessary first to determine the over-all reflection coenicient ofthe plug 39, referred, for example, to the left-hand surface of theplug. Thereafter by use of Equations 19- and 19a a spacing of the slabs4| and 42 may be determined which will give an equivalent reectioncoefficient referred to the left-hand surface of the slab 4|. Thisspacing will, of course, be a, function of the thickness and dielectricproperties of the respective plugs. Once the proper location of theplugs 4| and 42 with respect to one another is fixed, the distancebetween the left-hand surface. of the plug 39 and the correspondingsurface of the slab 4| required to assure destructive interference ofthe waves respectivelyreflected from the two reflecting` units may 13?be computed by an analysis similar to Lthat involved in the derivationof vEquation l22.

Fig. 9 represents the application of the invention to the case of a waveguide 43 which is terminally connected to a smaller wave guide 44. Dueto the difference-in dimensions of the.Y two Wave guide sections, theywill under ordinary circumstances have different characteristicimpedances and wave reflection will occur at their junction. `To annulthis reflection there are provided two identical dielectric slabs 45 and45 which are respectively spaced from one anotherA and from the entranceextremity of the waveguide 44.

In designing an arrangement such as that of Fig. 9, the composition ofthe plates t5 and 46 may be chosen rather arbitrarily with a View toemploying materials which are structurally suitable. Moreover, thethickness of theplates is arbitrary within relatively wide limits. Withthe impedance and the thickness of the plates given, it is possible tovary the spacing of the plates With reference to one another inaccordance with Equation 19 to produce a reflection coefficientl for thecombination which equals in absolute magnitude thecomputed or observedreilection coefficient of the boundary between the wave guide sections43 and 4i. Thereafter, the spacing of the left-hand surface of the plate5 with respect to the entrance extremity of the guide section de (i. e.,the reflecting boundary) must be adjusted to assure (2n-1)- phasedisplacement between the reflected waves Whose destructive interferenceis desired.

` In the wave guide construction of Fig. 9, the reflective slabs orplates may alternatively be located in the smaller wave guide sectiond4.'

A still further application of a multiple plate combination as areflection reducing agency is illustrated in Fig. 10. In this case thereis shown a coaxial conductor transmission line having an outer conductor5i! and an inner conductor 5I. The inner conductor terminates in anunshielded portion 5| which may be assumed to constitute a radiatingantenna or to connect with an antenna or other utilization device. It isobvious that the effective impedance of the unshielded section 5I willbe different from theimpedance of the transmission line combination, sothat wave reflection at their junction may be anticipated. To avoidthis, there are provided a pair of dielectric plates or disks 53, 511which are fitted into the conductor 59 and which have dimensions andspacings calculated in accordance with the principles previously givenherein to neutralize reflection from the transmission line termination.In connection with a coaxial transmission line system, the dielectricplates 53 and 54 of Fig. 10 may be replaced by equivalent transitionelements of a different structural character.` This possibility isillustrated in one embodiment in Fig. 11 which-shows a coaxialtransmission line having conductors 60 and 6l, the inner conductorterminating in an antenna section t l Attached to the conductor 6lwithin the confines of the conductor B are a, pair of annular conductive(e. g., metal) sleeves 63, E4 which are of similar dimensions and whichare mutually spaced.

It is apparent that each of the sleeves 63 and 64 introduces into thetransmission line system a short section (corresponding to the length ofthe sleeve in question) having an impedance which is different from thatof the transmission line proper. In this respect then, each of thesleeves is equivalent to one of the dielectric plates 53,' 54 .of Fig.9. Moreover, by, considerations 14v similar to those used in connectionwith the constructions of Figs. 5 to 10, one may determine thedimensions and spacing of the sleeves S3 and 64 which are required tocancel the reiiection occurring at the extremity of the transmissionline (i. e., at'its junction with the antenna BI).

A further .modification of this same principle is shown in Fig. 12 inwhich annular sleeves 13 and 14, functionally similar tothe sleeves B3and 64 of Fig. 11, are secured to the inner surface of a tubularconductor 'lll which forms the outer member of a coaxial'conductortransmission line. By appropriate choice of the dimensions and spacingsof the members 'i3 and 14, terminal reilections due to the junction ofthe transmission line with an antenna 'H' may be neutralized.

Reflection-preventing sleeves of the character illustrated in Figs. 11and 12 may also be used in connection with single pipe wave guides.However, in the latter application it is considered that dielectricslabs have an advantage over transition elements of other forms in thatthey have no tendency to introduce new types of waves (i. e., waves of aform diiferent from the form of the incident wave) In summary, it may besaid that in a large class of cases unwanted reflection from areflection-producing discontinuity may be cancelled or annulled byproviding in connection with the discontinuity a neutralizing systemhaving a reiection coefficient equal to that of the discontinuity andhaving a spacing with respect to the 'discontinuity such that at planesin advance of all the reflecting agencies a phase displacement ofapproximately mr radians exists between reections attributable to thediscontinuity and reflections attributable to the neutralizing system, nbeing an odd integer. It should be noted, however, that the question ofwhether the provision of equal reflection coelcients represents a propercondition for complete neutralization depends to some extent upon thenature of the reflecting agencies involved. More specifically, it is acondition which is applicable in an arrangement in which theneutralizing system is ahead of the discontinuity desired to beneutralized,.provided a-phase displacement of exists between wavecomponents reected by the system and wave components transmitted by thesystem. In other words, the relationship assumed in Equations l5 and 15amust be valid. Where the discontinuity is ahead of the neutralizingmeans (as in Fig. 8), then the discontinuity (and not necessarily theneutralizing means) must comply with the aforementioned relationship.

v A phase displacement of 90 between reected and transmitted componentsrepresents an assumption which is justified in the eventthereiiection-producing agency in question comprises a single,substantially non-dissipative, dielectric slab or a plurality ofidentical such slabs. It is not justified where the reflection-reducingsystem is made up of a number of dissimilar slabs or where it is made upof structural discontinuities such as those illustrated in Figs. 11 and12. Accordingly, in connection with reflection-reducing agencies of thelatter class, it will be found that for complete neutralization rto beobtained the reflection coefficient of the neutralizing means mustordinarily be somewhat different from the reflection coeflicient of thediscontinuity which give-s rise to fthe reiiections desired to beannulled. This qualification also applies in cases' While the.inventionhasbeen described by reference to particular applications andspecific embodiments, it will be understood that numerous modificationsmay be made by those .slcilled' inthe art without departing from theinvention. We, therefore, aim inthe appended claims to` cover all suchequivalent variations of.' structure or use as, come within the truespirit and scope of the; foregoing disclosure.

What we claim as new and-desire to secure by Letters Patent of theUnited States is.:

1. An electromagnetic system. for propagating centimeter wavescomprising a wave-propagating structure having a discontinuity at whichreflection tends to occur, and means in proximity to said discontinuityand in the path of wave propagation for annulling the said reflection,said means comprising the combination of a plurality of spaced elementseach constituting in itselfV a short section of wave-propagatingstructure and having a thickness in the direction of wave propagationwhich is a material fraction of the Wave length of the waves to bepropagated whereby,l the overall reflection from said combination isdefined by a reflection coefllcientin which both the spacing andthickness of the elements enter as dominant factors, the spacing of saidelements with respect to one anotherl being so adjusted that at anyplane in said structure located in advance of the said elements and thevsaid dis'- continuity with reference to the direction of wavepropagation the rellection attributable to the elements is equal to thatattributable .to the said discontinuity, and the spacing of saidelements with respect to the discontinuity being such that at the saidplane a phase displacement of approximately mr radians exists betweenreflections attributable to :the discontinuity and reflectionsattributable to the elements, n being an odd integer.

2. An electromagnetic system for propagating centimeter waves comprisinga wave-propagating structure having a discontinuity at which reflectiontends to occur, and means in proximity to the said discontinuity and inthe path of wave means comprising the combination of a plurality ofspaced dielectric plates each having a thick-` ness which is a materialfraction of the wave length of the waves to be propagated whereby theoverall reflection from said combination is dened by a reflectioncoefficient in which both the spacing and thickness of the plates hasdominant factors, the spacing of said plates with respect to one anotherbeing so adjusted that at any plane in said structure located in advanceof the said plates and the said discontinuity with reference to thedirection of wave propagation the reflection attributable to .the platesis equal to that attributable to the said discontinuity, and the spacingof said plates-with respect to the discontinuity .being such that at thesaid plane a phase displacement of approximately mr radians existsbetween reflections attributable to the discontinuity and reflectionsattributable to the plates, n being: an odd integer.

3. An electromagnetic system for propagating centimeter `wavescomprising a wave-propagating structure having a discontinuity at whichreflection tends to occur in an amount determined by a reilectioncoeicient assignable to the discontinuity, and means for annulling thesaid reflection, said means comprising the combination of a pluralityofV identical dielectric plates located in advance of the said discontinuity with reference to the direction of Wave propagation andeachhaving a thickness which is amaterialV fraction ofl the wave lengthofV the waves'to be propagatedY whereby the overall reection from saidcombination is defined. by a reflection coefficient in which both thespacing and thickness of the plates enter as dominant factors, thespacing of said plates with respect to one another Abeing adjusted toproduce a reflection coeihcient for the combination equal to that of thesaid discontinuity, and the spacing of said plates with respect to thediscontinuity being such that at any plane in said structure located in`advance of the said plates a phase displacement of approximately mrradians exists between. reflections attributable to the discontinuityand reections attributable to the said plates, n being an odd integer.

4. In combination, a source of centimeter waves, a wave guide connectingwith said source for propagating waves derived from the source, andmeans for annulling the reflection of waves at the junction between saidsource and said wave guide, said last-named means comprising accmbination of spaced dielectric plates which are located within saidwave guide in proximity to the said junction and which are of athickness corresponding to a material fraction of the wave length of thewaves derived from said source whereby the overall reflection from saidcombination is defined by a reflection coelcient in which both thespacing and thickness of the plates enter as dominant factors, thespacing of said plates with respect to one another being so adjustedthat at a plane between the said source and the said junction thereflection attributable to the plates is equal to that attributable tothe junction, and the spacing of said plates with respect to thejunction being such that at the said plane a phase displacement ofapproximately ne radians exists between reflections attributable to thejunction and reflections attributable to the plates, n being an oddinteger.

5. In combination, a hollow conductive wave guide defining a firstpropagating region, means adjoining said wave guide and defining asecond propagating region of different characteristic impedance than therst, and a plurality of identical dielectric plates successivelyarranged in advance of the junction of said iirst and second regions forfacilitating the reilectionless transfer of wave energy between theregions, the dimensions and spacing of said plates with respect to oneanother being such that the overall reflection coeillcient resultingfrom their combination is equal to the reflection coefficient of thesaid junction, and the spacing between the junction and the plates beingsuch that with respect to waves which pass through the various plates,are reflected at the said junction and retraverse the plates, the phaseshift attributable to said spacing plus the phase shift attributable tothe plates themselves differs by approximately mr radians from the phaseshift of waves reflected directly from the first of said plates, n beingan odd integer.

6. In an electromagnetic system which is adapted to propagate centimeterwaves and which comprises two adjacent propagating regionsV of differentcharacteristic impedance; an arrangement which includes at least twospaced elements in proximity to the junction of the said regions and inthe path of the propagated waves for assisting the non-reflectivetransfer of wave energy from one region to the other, each of saidelements constituting a short section of Wave-propagating structure andbeing of a thickness which is a material fraction of the Wave length ofthe waves desired to be propagated by the system whereby the overallreiiection from said arrangement is defined by a reiiection coefficientin which both the spacing and thickness of the elements enter asdominant factors, the spacing of said elements with respect to oneanother being so adjusted that at a plane locate-:l in advance of thesaid elements and the said junction with reference to the direction ofWave propagation the reiection attributable to the elements is equal tothat attributable to the junction, and the spacing of said elements withrespect to said junction being adjusted to secure phase oppositionbetween Said reiections to obtain destructive interference thereof.

7. In an electromagnetic system, an elongated hollow Wave conningstructure denning a first Wave-propagating region, and means forfacilitating the transfer of Wave energy from said region. to a secondregion of different eiective impedance, said means comprising aplurality of 18 localized constrictions provided within said structureat mutually displaced points near its junction with said second region,the extension of said constrictions in the direction of wave propagationcomprising a material fraction of the wave length of the Waves desiredto be propagated whereby the overall reflection of the 'variousconstrictions is donned by a reilecticn coenicient in which both thespacing and extension of the constrictions enter as dominant factors,the spacing of said constrictions with respect to one another being soadjusted that at a plane located in advance of the said constrictionsand the said junction with reference to the direction of propaga,- tionthe reflection attributable to the constructions is equal to thatattributable to the junction, and the spacing of the constrictions withrespect to the junction being such that at the said plane a phasedisplacement of approximately 1inradians exists between reflectionsattributable to the junction and reflections attributable to theconstrictions, n being an odd integer.

LEWI TONKS. LE ROY APKER.

